10.31124/advance.7222010.v1
Uri Simonsohn
Two-Lines: A Valid Alternative to the Invalid Testing of U-Shaped Relationships with Quadratic Regressions
2018
Advance
quadratic
non-linear
u-shape
monotonic
too much talent
two-lines
2018-10-25 18:28:28
article
https://advance.sagepub.com/articles/Two-Lines_A_Valid_Alternative_to_the_Invalid_Testing_of_U-Shaped_Relationships_with_Quadratic_Regressions/7222010
Many psychological theories predict U-shaped relationships: the effect of x is positive for low values of x, but negative for high values, or vice-versa. Despite implying merely a change of sign, hypotheses about U-shapes are tested almost exclusively via quadratic regressions, imposing an arbitrary functional form assumption that can lead to a 100% false-positive rate, e.g., concluding with certainty that y=log(x) is U-shaped. Estimating two regression lines, one for low and one high values of x, allows testing for a sign change without a functional form assumption. To set the breakpoint between the lines, I introduce the Robin Hood algorithm. It delivers higher power to detect U-shapes than all other breakpoint setting alternatives considered. The paper includes simulations and re-analyses of published results. The two-line test can be performed at http://webstimate.org/twolines